1Introduction & how to read this document

The sea has no signposts. For most of history a mariner out of sight of land had no fixed landmarks against which to judge how far, how fast, or in which direction the ship was moving. Out of that problem grew a distinctive family of units — the nautical mile, the knot, the fathom, the Beaufort force — each tied not to an arbitrary human artefact but, wherever possible, to the geometry of the Earth itself. That is what makes them endure: a single minute of arc on the globe is the same for a Phoenician galley and a modern container ship.

This document defines the quantities and units a navigator uses day to day, gives the symbol(s) in current international use, and explains why each unit exists and where it came from. Every factual claim is backed by a numbered, clickable reference in Section 9. Values follow the modern international standards of the International Hydrographic Organization (IHO), the World Meteorological Organization (WMO), and the International Bureau of Weights and Measures (BIPM).

A note on symbols

The nautical mile has no single symbol agreed across all bodies: the IHO uses M, the ICAO uses NM, and the IEEE / US Government Publishing Office use nmi. The lower-case nm is common at sea but formally clashes with the SI nanometre, so it is avoided in scientific text. This document uses NM throughout for clarity. [11]

2Distance & length at sea

2.1  Nautical mile — NM (also M, nmi)

Definition. The nautical mile is a unit of distance for sea and air navigation defined by international agreement as exactly 1 852 metres (≈ 6 076 ft ≈ 1.151 statute miles). It is not part of the SI system but is accepted for use with it. [1][4][11]

Why it exists. The nautical mile was built to equal one minute of arc of latitude (1/60 of a degree) along a meridian. Because a circle of the Earth is divided into 360° and each degree into 60′, the meridian is divided into 360 × 60 = 21 600 nautical miles. This gives the navigator an extraordinary convenience: distance can be read straight off the latitude scale on the side of a chart with a pair of dividers, with no conversion factor at all — one minute of latitude is one nautical mile. [1][6]

History. Because the Earth is an oblate spheroid (flattened at the poles), a minute of latitude is not constant — it runs from about 1 843 m at the Equator to about 1 862 m near the poles. [4][7] For centuries nations therefore used slightly different values (the British 6 080 ft "Admiralty mile", the US value based on the Clarke 1866 ellipsoid, and so on), which caused confusion in international shipping. France derived a value from the 1791 definition of the metre — one ten-millionth of the quarter meridian — giving 10 000 000 / 90 / 60 ≈ 1 851.85 m. [7] The First International Extraordinary Hydrographic Conference (Monaco, 1929) fixed the rounded international value of exactly 1 852 m. The United States adopted it in 1954 and the United Kingdom in 1970, making it universal. [1][4][7]

2.2  Geographical mile — mi (geo.)

Definition. The geographical mile is the length of one minute of arc of longitude measured along the Equator. For the international (WGS-84 / GRS-80) ellipsoid this is about 1 855.3 m. [1]

Why it differs from the nautical mile. The nautical mile is tied to a minute of latitude (along a meridian); the geographical mile is tied to a minute of longitude at the Equator, where the Earth's radius is largest. Because the equatorial circle is slightly bigger than a meridian, the geographical mile is a few metres longer than the nautical mile. It appears on older charts and in some legal texts (this matches the "mile geographical = 1855,3 m" entry on the source table). [1]

2.3  Cable (cable length) — cbl

Definition. A cable length is a short-range distance unit equal to one tenth of a nautical mile — i.e. 185.2 m. The traditional British/US value of 100 fathoms (≈ 182.9 m) or 120 fathoms (≈ 219.5 m) also survives in older sources; the source table's "1 cable = 720 feet = 219.456 m" reflects the older 120-fathom naval cable. [10][49]

Why it exists. Cables bridge the awkward gap between metres and nautical miles for close-quarters work — ranges to buoys, distances off a hazard, or a ship's turning circle. The name comes literally from the length of anchor cable once carried aboard ship. [50]

2.4  Fathom — fth (fm)

Definition. The fathom is the traditional unit of water depth, standardised at 6 feet = 1.8288 m. [53][55]

History. "Fathom" comes from the Old English fæðm ("outstretched / embracing arms"): the earliest fathom was literally the span from fingertip to fingertip of a large man's outstretched arms — because that is exactly how a sailor hauled in a sounding line, measuring it arm-span by arm-span as the lead weight came up. [48][53][56] Arm-spans varied, so nations fixed their own values before the modern 6-foot standard settled the matter. Fathoms still appear on many charts (especially US waters) and on echo-sounder displays. [54]

Related depth conventions: cable depth (an old sounding cable of 720 ft = 219.456 m) and the shackle for anchor chain (below).

2.5  Shackle (shot) — anchor-chain length

Definition. A shackle is the standard length of a link-section of anchor chain, equal to 15 fathoms = 90 feet = 27.432 m (the international/Imperial "shackle"; the US Navy "shot" is 15 fathoms as well). [49]

Why it exists. Anchor cable is manufactured and joined in these fixed sections, marked with paint and turns of wire at each shackle so that the crew can call out how much chain has been "veered" (paid out) — e.g. "four shackles in the water". Scope is reckoned in shackles for safe anchoring. [49]

2.6  Length & distance — quick reference

3Speed

3.1  Knot — kn (kt)

Definition. The knot is the unit of speed at sea and in the air, equal to one nautical mile per hour: 1 kn = 1 NM/h = 1.852 km/h ≈ 0.514 m/s. [10][11]

Why speed is measured in knots — the chip log. The name is literal. From the late 16th century a ship's speed was measured with a chip log: a weighted, pie-slice-shaped board ("chip") on a long line that was thrown over the stern. The board stayed roughly stationary in the water while the line ran out as the ship sailed on. The line was tied with knots at regular intervals; a sailor counted how many knots ran out during a fixed interval timed by a sand-glass (about 28–30 s). The number of knots that passed = the ship's speed in nautical miles per hour — hence "knots". [10][14][17]

The spacing was chosen to make the arithmetic exact. Knots tied roughly every 14.4 m (≈ 47 ft 3 in) and a 28-second glass give: (14.4 m × 3600 s) / 28 s ≈ 1 852 m/h = 1 NM/h per knot counted. Earlier, cruder methods included the Dutchman's log — throwing a floating object off the bow and timing how long the ship took to pass it. Modern ships use electromagnetic, Doppler or pressure (pitometer) logs, but the unit — and the name "log" for a speed instrument — survives. [10][14][19]

3.2  Speed over ground vs. speed through the water

STW (speed through the water) is what a log measures — the ship's motion relative to the surrounding water. SOG (speed over ground) is motion relative to the seabed/Earth, as given by GPS. They differ by the current: a 10 kn ship steaming into a 2 kn current makes only 8 kn over the ground. The distinction matters for ETA and fuel, and is the speed analogue of the course distinction in Section 5. [58][59]

4Position — latitude & longitude

A position at sea is given as a pair of angles measured from the centre of the Earth: latitude (north–south) and longitude (east–west). The grid concept dates at least to the geographer Ptolemy (≈ AD 150). [51]

4.1  Latitude — Lat, φ

Definition. Latitude is the angular distance of a point north or south of the Equator, from 0° at the Equator to 90° N or 90° S at the poles. Lines of equal latitude (parallels) run east–west. [49][51]

Why it is easy to find. Latitude can be found from a single local observation — the noon altitude of the Sun, or the altitude of Polaris — which is why it was reliably measured for centuries before longitude could be. This is also the axis that ties directly to distance: 1′ of latitude = 1 NM. [51][56]

4.2  Longitude — Lon, λ

Definition. Longitude is the angular distance east or west of a reference meridian — since 1884 the Greenwich (Prime) Meridian — from 0° to 180° E or W. Lines of equal longitude (meridians) run north–south and converge at the poles. [51][52]

The longitude problem. Longitude cannot be found from altitude alone; it requires knowing the time difference between the ship and a reference meridian (the Earth turns 15° of longitude per hour). Solving this took centuries and was cracked only when John Harrison built the first practical marine chronometer in the 18th century, which — combined with sextant sights — finally let mariners fix both coordinates reliably. [56][52]

5Direction, heading & course

Direction at sea is an angle measured clockwise from north, 000° to 359° (three digits, always). The subtlety is that there are three different "norths" and several different "directions" a navigator must keep distinct. [43]

5.1  The three norths: True, Magnetic, Compass

True north (T) points to the geographic North Pole — the axis the chart's grid is drawn to. Magnetic north (M) is where a compass needle points, toward the magnetic pole, which does not coincide with the geographic pole. Compass north (C) is where the needle actually points on your particular ship, once local iron and electronics have tugged it further off. [43][44]

Variation (declination). The angle between true and magnetic north, measured east or west. It depends on geographic position, is printed inside the compass rose on each chart, and changes slowly over years as the magnetic pole drifts. On an agonic line, variation is zero. [40][41][46]

Deviation. The angle between magnetic and compass north, caused by the ship's own magnetic field (steel hull, engine, wiring, electronics). Unlike variation it is unique to each vessel and changes with the ship's heading; it is recorded on a deviation card produced by "swinging" the ship. [40][41][44]

Converting between them (TVMDC). Navigators chain the corrections True → Variation → Magnetic → Deviation → Compass. A common memory aid is "True Virgins Make Dull Companions — Add Whisky", where westerly errors are added going from true to compass. [47][43]

5.2  Heading, bearing, course

Heading (HDG) is the direction the ship's bow is pointing at this instant. Course is the direction you intend to travel (course to steer) or have plotted on the chart. Bearing (BRG) is the direction to another object (a lighthouse, another ship) from your position. Heading and course differ whenever wind or current pushes the vessel sideways. [42][43]

Course Over Ground (COG) & Course Made Good (CMG). Because current and leeway carry the ship off the direction it is pointing, the actual track over the seabed — the COG from GPS — differs from the heading. The navigator's job is to choose a heading that makes the COG equal the desired course. [43]

5.3  Set, drift & leeway

Set is the direction toward which a current flows; drift is its speed. Leeway is the sideways slip caused by wind on the hull and rig. Together they are the difference between where the bow points and where the ship actually goes — the reason heading and course-made-good rarely match exactly. [61]

5.4  Rhumb line vs. great circle

A rhumb line (loxodrome) crosses every meridian at the same angle, so it is a track of constant compass bearing — simple to steer. On a Mercator chart it appears as a straight line, which is exactly why Mercator's 16th-century projection became the standard for nautical charts. [58][61][62]

A great circle (orthodrome) is the intersection of the Earth's surface with a plane through the planet's centre; it is the shortest distance between two points on a sphere. Its drawback is that its bearing changes continuously, so it must be steered as a series of short rhumb-line legs. On long ocean or air routes the great circle can be dramatically shorter, so it is preferred there; over short distances the two nearly coincide. [58][62]

6Depth & soundings

Depth (a "sounding") is the vertical distance from the water surface to the seabed. Historically it was taken with a lead line — a lead weight on a marked line — and read in fathoms (Section 2.4); the Viking sailor measured the recovered line by his arm-span, the very act that named the fathom. [56] Charts reduce soundings to a chart datum (a low-tide reference) so the depths shown are the shallowest a mariner should expect. [57]

Modern vessels use an echo sounder (single- or multi-beam sonar), which times an acoustic pulse to the bottom and back. Chart soundings may be printed in metres, fathoms, or feet depending on the chart's origin, so the units block on the chart must always be checked. [57]

7Weather & wind — the Beaufort scale

Definition. The Beaufort wind force scale is an empirical scale that relates wind speed to observable effects on the sea (and on land), running from Force 0 (calm) to Force 12 (hurricane). It lets a mariner estimate wind strength by eye — from ripples, whitecaps, spray and wave height — without any instrument. [20][22][24]

History. It was devised in 1805 by Commander (later Rear-Admiral Sir) Francis Beaufort, an Irish-born hydrographer of the British Royal Navy, while serving aboard HMS Woolwich. His aim was to replace the hopelessly subjective log entries of the day — one officer's "stiff breeze" was another's "gentle" one — with numbered forces 0–12. The scale was originally calibrated to the amount of sail a full-rigged man-of-war could carry in each wind. [21][23][27]

The British Admiralty made it mandatory in Royal Navy logs in 1838, and it was famously used on the voyage of HMS Beagle under FitzRoy (with Darwin aboard). It was adopted for international weather telegraphy by the International Meteorological Committee in 1874. Descriptions were extended to conditions on land (1906), tied to equivalent wind speeds (1926), and to reporting in knots (1946–47). Forces 13–17 were added in 1946 for tropical cyclones but are little used outside East Asia. [20][22][28]

7.1  The Beaufort scale — Force 0 to 12

7.2  Sea state code (WMO 0–9)

Alongside Beaufort, the WMO sea state code describes the water surface itself by significant wave height (the mean height of the highest one-third of waves) on a scale of 0 (calm, glassy) to 9 (phenomenal, > 14 m). Sea state and Beaufort force are correlated but distinct: swell left over from a distant storm can give a rough sea in a light wind. [32][33][37]

8Master reference — quantities, units & symbols

9References (clickable)

All links verified against primary or authoritative secondary sources (standards bodies, national weather services, museums, encyclopaedias and peer-reviewed / institutional pages).

1. 1Nautical mile — definition, history & 1929 standardisation — Encyclopædia Britannica. britannica.com/science/nautical-mile
2. 4Nautical mile — value, oblate-spheroid variation, adoption dates — Encyclopædia Britannica. britannica.com/science/nautical-mile
3. 6One minute of arc = 1 NM; reading distance off the latitude scale — Foresmart. foresmart.com/what-is-a-nautical-mile
4. 7Metric origin (1791 metre), Clarke 1866, national values, 1929 — Nautical mile — Wikipedia. en.wikipedia.org/wiki/Nautical_mile
5. 10Knot = 1 NM/h; chip log; belay / hand-the-log procedure — Royal Museums Greenwich. rmg.co.uk — Knots: measuring speed at sea
6. 11Symbols M / NM / nmi; SI status; knot as derived unit — EPFL GraphSearch. graphsearch.epfl.ch — nautical mile
7. 14Chip log as first speedometer; 14.4 m knot spacing; 28-s glass — MIT School of Engineering. engineering.mit.edu — Ask an Engineer
8. 17Chip log / common log; origin of "knot"; Dutchman's log — Chip log — Wikipedia. en.wikipedia.org/wiki/Chip_log
9. 19"Log" as the name for any speed instrument; pitometer log — Pitometer log — Wikipedia. en.wikipedia.org/wiki/Pitometer_log
10. 20Beaufort history; 1874 international adoption; extensions — Hong Kong Observatory. hko.gov.hk — Beaufort Wind Scale
11. 21Scale devised 1805; mandatory in RN logs 1838; man-of-war basis — Encyclopædia Britannica. britannica.com/science/Beaufort-scale
12. 22Empirical scale; Francis Beaufort 1805; Royal Navy adoption — Beaufort scale — Wikipedia. en.wikipedia.org/wiki/Beaufort_scale
13. 231805 origin; non-instrumental estimation from a man-of-war — U.S. Naval Institute, Proceedings (1934). usni.org — Beaufort Wind Scale
14. 24Beaufort scale; HMS Woolwich; 10-min mean at 10 m — Royal Meteorological Society. rmets.org — Beaufort Wind Scale
15. 27Standardising subjective wind terms; adoption in the 1830s — Skipper's Online (PDF). skippersonline.net — Beaufort (PDF)
16. 28Refinement to 12 forces; HMS Beagle; 1939 international form — Grokipedia. grokipedia.com/page/Beaufort_scale
17. 30Beaufort table; mean speeds; wind measured at 10 m — Royal Meteorological Society. rmets.org — Beaufort Wind Scale
18. 32Forces 11–12 seas; 1946 extension (13–17); significant wave height — Solar Navigator. solarnavigator.net — Sea state / Beaufort
19. 33Beaufort to F12; higher levels 13–17; significant wave height — ScienceDirect Topics. sciencedirect.com — Beaufort scale
20. 34Full table with knots & wave heights; NWS warning thresholds — CalcSpec (WMO/NOAA). calcspec.com — Beaufort wind scale
21. 37Met Office Beaufort table (knots, m s⁻¹, wave height, sea state) — UK Met Office. metoffice.gov.uk — Beaufort scale
22. 38Beaufort visual clues, wind speed & wave height per force — US National Weather Service (PDF). weather.gov — Beaufort (PDF)
23. 39Marine wind & sea threat levels tied to Beaufort force — US National Weather Service. weather.gov/mlb/windsea_threat
24. 40Variation vs deviation; deviation varies with heading — Savvy Navvy. savvy-navvy.com — Variation & Deviation
25. 41Variation, deviation, agonic lines, secular change — Amnautical. amnautical.com — Variation vs Deviation
26. 42Course vs heading; variation & deviation formulae — Pilot Mall. pilotmall.com — TC / TH / MH
27. 43Three norths; true/magnetic/compass course; COG/CMG — Sailing Issues. sailingissues.com — Nav course 3
28. 44Deviation defined; "swinging" the ship; easterly / westerly — Maritime SA. maritimesa.org — Variation, deviation
29. 46Declination / variation; isogonic & agonic lines; deviation — SKYbrary. skybrary.aero — Magnetic Variation
30. 47TVMDC conversion; worked variation / deviation example — Marine Public. marinepublic.com — Variation & Deviation
31. 48Fathom = 6 ft ≈ 1.83 m; Old English fæðm ("embrace") — UK Sailmakers. uksailmakers.com — Fathom
32. 49Latitude/longitude; fathom 1.8288 m; shackle 15 fth = 27.432 m — Maritime Page. maritimepage.com — Nautical Units
33. 50Knots, fathoms & the language of nautical measurement — boats.com. boats.com — Knots, fathoms & gales
34. 51Latitude/longitude concept; Ptolemy; oblateness; 1′ lat = 1 NM — Univ. of Wisconsin — Oceans. aos.wisc.edu — Oceans supplement
35. 52The centuries-long "longitude problem" — History of longitude — Wikipedia. en.wikipedia.org/wiki/History_of_longitude
36. 53Fathom standardised at 6 ft (1.83 m); anatomical origin — Encyclopædia Britannica. britannica.com/science/fathom
37. 54Fathom etymology; national variation; US chart use — UT Marine Science Institute. utmsi.utexas.edu — Nautical Nomenclature
38. 55Fathom = 1.8288 m; Middle / Old English & Danish cognates — Wayne Savage. waynesavage.com — Nautical units of distance
39. 56Harrison's chronometer; lead-line soundings; fathom origin — Encyclopædia Britannica — Navigation. britannica.com — Navigation (Longitude)
40. 57Reading charts; soundings in feet / fathoms / metres; datum — Better Boat. betterboat.com — Reading nautical charts
41. 58Great circle vs rhumb line; Mercator; constant bearing — Mapscaping. mapscaping.com — Great circles & rhumb lines
42. 59Speed made good / VMG; boat speed over ground — Ocean Sail. oceansail.co.uk — VMG article
43. 61Rhumb line / loxodrome; constant azimuth; set & drift — Rhumb line — Wikipedia. en.wikipedia.org/wiki/Rhumb_line
44. 62Great circle = shortest path; changing bearing; Mercator — Kavas. kavas.com — Great circle vs rhumb line

Standards bodies referenced: International Hydrographic Organization (IHO) · World Meteorological Organization (WMO) · International Bureau of Weights and Measures (BIPM) · International Civil Aviation Organization (ICAO). Historical values (e.g. the 720-ft cable, 6 080-ft Admiralty mile) are noted where they differ from modern SI-based figures.

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